Exact separation of surface and bulk contributions to anisotropic second-harmonic generation from cubic centrosymmetric media

We solve this long-standing problem theoretically by recognizing that the ranks of the tensors that describe the surface and bulk second-order nonlinear susceptibilities differ in this class of media. We show that this implies that the phenomenologies of the anisotropic optical second-harmonic (SH) responses of the two sources differ for all possible crystal facial orientations except (111). To demonstrate the result, we apply the theory to separate the surface and bulk contributions to SH generation from an oxidized vicinal Si(001) wafer for p-polarized 775-nm fundamental and s-polarized SH radiation. It is shown that knowledge of the phase of the SH field is necessary to achieve a unique separation.